GATE-CH-1991-7-i-td-2mark

For a gas obeying the van der Waals equation, at the critical temperature

• both \((\partial P/\partial V)_T\) and \((\partial ^2P/\partial V^2)_T\) are zero

• the first derivative is zero, while the second derivative is non-zero

• the second derivative is zero, while the first derivative is non-zero

• both the derivatives are non-zero

GATE-CH-1994-1-s-td-1mark

Ideal gas law is applicable at

• low \(T\), low \(P\)

• high \(T\), high \(P\)

• low \(T\), high \(P\)

• high \(T\), low \(P\)

GATE-CH-1995-1-l-td-1mark

A solid is transformed into vapor without going through the liquid phase at

• triple point

• boiling point

• below triple point

• always

GATE-CH-1999-1-7-td-1mark

Which of the following is true for virial equation of state?

• Virial coefficients are universal constants

• Virial coefficient \(B\) represents three body interactions

• Virial coefficients are functions of temperature only

• For some gases, virial equations and ideal gas equations are the same

GATE-CH-2002-1-3-td-1mark

Which of the following conditions are satisfied at the critical point by the \(PVT\) relation of a real fluid?

• \(\displaystyle \left (\frac {\partial ^2P}{\partial V^2}\right )_T = \left (\frac {\partial P}{\partial V}\right )_T=0\)

• \(\displaystyle \left (\frac {\partial ^2P}{\partial V^2}\right )_T >0, \quad \left (\frac {\partial P}{\partial V}\right )_T=0\)

• \(\displaystyle \left (\frac {\partial ^2P}{\partial V^2}\right )_T <0, \quad \left (\frac {\partial P}{\partial V}\right )_T=0\)

• \(\displaystyle \left (\frac {\partial ^2P}{\partial V^2}\right )_T >0, \quad \left (\frac {\partial P}{\partial V}\right )_T>0\)

GATE-CH-2006-35-td-2mark

The molar density of water vapor at the normal boiling point of water is 33 mol/m³. The compressibility factor under these conditions is close to which ONE of the following? \(R=8.314\) J/(mol.K)

• 0.75

• 1

• 1.25

• 1.5

GATE-CH-2007-8-td-1mark

Parameters '\(a\)' and '\(b\)’ in the van der Waals and other cubic equations of state represent

• \(a\) - molecular weight;  \(b\) - molecular polarity

• \(a\) - molecular size;  \(b\) - molecular attraction

• \(a\) - molecular size;   \(b\) - molecular speed

• \(a\) - molecular attraction;  \(b\) - molecular size

GATE-CH-2008-7-td-1mark

The work done by one mole of a van der Waals fluid undergoing reversible isothermal expansion from initial volume \(V_i\) to final volume \(V_f\) is

• \(\displaystyle RT\ln \left (\frac {V_f}{V_i}\right )\)

• \(\displaystyle RT\ln \left (\frac {V_f-b}{V_i-b}\right )\)

• \(\displaystyle RT\ln \left (\frac {V_f-b}{V_i-b}\right ) -a\left (\frac {1}{V_f}-\frac {1}{V_i}\right ) \)

• \(\displaystyle RT\ln \left (\frac {V_f-b}{V_i-b}\right ) +a\left (\frac {1}{V_f}-\frac {1}{V_i}\right ) \)

GATE-CH-2013-8-td-1mark

The units of the isothermal compressibility are

• m^-3

• Pa^-1

• m³.Pa^-1

• m^-3.Pa^-1

GATE-CH-2017-6-td-1mark

The volumetric properties of two gases M and N are described by the generalized compressibility chart which expresses the compressibility factor (\(Z\)) as a function of reduced pressure and reduced temperature only. The operating pressure (\(P\)) and temperature (\(T\)) of two gases M and N along with their critical properties (\(P_c,T_c\)) are given below.

Gas	\(P\) (bar)	\(T\) (K)	\(P_c\) (bar)	\(T_c\) (K)
M	25	300	75	150
N	75	1000	225	500

\(Z_{\text {M}}\) and \(Z_{\text {N}}\) are the compressibility factor of the gases M and N under given operating conditions, respectively.

The relation between \(Z_{\text {M}}\) and \(Z_{\text {N}}\) is

• \(Z_{\text {M}}=8Z_{\text {N}}\)

• \(Z_{\text {M}}=3Z_{\text {N}}\)

• \(Z_{\text {M}}=Z_{\text {N}}\)

• \(Z_{\text {M}}=0.333Z_{\text {N}}\)

GATE-XE-2008-G-14-td-2mark

Steam of quality 0.98 is present in two separate containers \(A\) and \(B\) at 300 kPa and 200 kPa, respectively. Specific volumes of steam in containers \(A\) and \(B\) initially are \(V_{A_1}\) and \(V_{B_1}\), respectively. Steam condenses at a constant pressure in such a way that the final quality of steam in both the containers are 0.01 and specific volumes of steam in containers \(A\) and \(B\) are \(V_{A_2}\) and \(V_{B_2}\) respectively. Which one of the following statements is true?

• \(V_{A_1}>V_{B_1}\) & \(V_{A_2} > V_{B_2}\)

• \(V_{A_1}<V_{B_1}\) & \(V_{A_2} < V_{B_2}\)

• \(V_{A_1}>V_{B_1}\) & \(V_{A_2} < V_{B_2}\)

• \(V_{A_1}<V_{B_1}\) & \(V_{A_2} > V_{B_2}\)

GATE-XE-2011-E-9-td-1mark

Consider three identical tanks A, B and C shown below. What is the pressure (\(P\)) in Tank C ?

• 1 bar

• 1.5 bar

• 2 bar

• 2.5 bar

GATE-XE-2018-E-5-td-1mark

The value of the compressibility factor at the critical point evaluated using the van der Waals equation of state is

• \(2/7\)

• \(5/8\)

• \(3/8\)

• \(1/7\)

GATE-CH-1993-6-6-td-1mark

A vessel of volume 1.0 m\(^3\) contains a mixture of liquid water and steam in equilibrium at 1.0 bar. Given that 90% of the volume is occupied by the steam, find the dryness fraction of the mixture.
Assume, at 1 bar, \(V_L = 0.001\) m\(^3\)/kg and \(V_V = 1.7\) m\(^3\)/kg.

• Answer

GATE-CH-1993-6-8-td-2mark

In the vicinity of the triple point, the vapor pressures of liquid and solid ammonia are respectively given by \[ \ln P = 15.16 - \frac {3063}{T} \quad \text { and } \quad \ln P = 18.70 - \frac {3754}{T} \] where \(P\) is in atmospheres and \(T\) is in Kelvin.
(i) What is the temperature (in K) at the triple point?
{#1}

(ii) What is the triple point pressure (in atm)?
{#2}

GATE-CH-2004-42-td-2mark

A vessel of volume 1000 m³ contains air which is saturated with water vapor. The total pressure and temperature are 100 kPa and 20^oC, respectively. Assuming that the vapor pressure of water at 20^oC is 2.34 kPa, the amount of water vapor (in kg) in the vessel is approximately

• 17

• 20

• 25

• 34

0200-1-td-5mark

Calculate the molar volume of saturated liquid and saturated vapor of propane at 40\(^\circ\)C and saturation pressure of 13.71 bar, using (i) ideal gas equation (ii) van der Waals equation (iii) Redlich-Kwong equation. \(T_c=369.8\) K; \(P_c = 42.5\) bar. 

• Answer